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I'm working in a project that uses"blade solidity ratio", or "rotor solidity", the problem is, there are several articles which defines the equation in a different way changing in the section of the Radius analysis. I found 3 equations that I will describe below:

$$1. \frac{Nc}{2πR}$$ $$2. \frac{Nc}{2R}$$ $$3. \frac{Nc}{R}$$ N=Number of Blades, c= Chord Length, R= Radius of the rotor

Which one is correct or there is some case where each of this equation is applied? Thanks.

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Rotor solidity is the area of the rotor disk that is actually occupied by blade area.

Area of rotor blades = $N \cdot c \cdot R$

Area of rotor disk = $\pi \cdot R^2$

$$Rotor \ solidity = \frac{N \cdot c}{\pi \cdot R} \tag{4}$$

So all three of the equations OP found would not be usual. Good reference books are:

  • Helicopter Performance, Stability and Control by Raymond R. Prouty
  • Principles Of Helicopter Aerodynamics by J. Gordon Leishman.

Both these books use equation (4) for rotor solidity. It is possible for a factor 2 to pop up in the coefficients which are usually considered regarding disk area and solidity: $C_T, C_P$ and $C_Q$. From Leishman:

enter image description here

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  • $\begingroup$ This is generally correct, but if a paper defines it differently and then presents results with respect to it, then that definition should be used for those results/formulae. I've also seen different definitions of solidity (usually for aeroplane propellers though), presumably to account for typical blade shapes etc. $\endgroup$ – Zeus Jul 17 '19 at 0:34
  • $\begingroup$ Thanks for your response, this was very helpful. $\endgroup$ – Resou Jul 17 '19 at 15:10
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Dimensionally, those expressions are the same (and thus comparable), except of course for the $2\pi$ constant.

Check the rest of the equations, it is very likely the numeric factor is simply elsewhere.

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